352edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:31:59Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:31, 13 March 2026
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	\| [[World calendar]]		\| [[World calendar]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

Francium: changed EDO intro to ED intro

2025-02-21T06:23:45Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:23, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|352~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:48, 15 January 2025

2025-01-15T17:48:20Z

← Older revision		Revision as of 17:48, 15 January 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	352 factors into ~~2<sup>5</sup> × 11~~, with subset edos {{EDOs\| 2, 4, 8, 11, 16, 22, 32, 44, 88, and 176 }}.		352 factors into {{factorisation\|352}}, with subset edos {{EDOs\| 2, 4, 8, 11, 16, 22, 32, 44, 88, and 176 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 84:		Line 84:
	\| [[World calendar]]		\| [[World calendar]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

ArrowHead294: Partial undo

2024-11-16T13:11:29Z

Partial undo

← Older revision		Revision as of 13:11, 16 November 2024
Line 12:		Line 12:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3.5		\| 2.3.5
Line 27:		Line 36:
	\| 0.2500		\| 0.2500
	\| 7.33		\| 7.33
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
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	\| 34/27<br />(18/17)		\| 34/27<br />(18/17)
	\| [[World calendar]]		\| [[World calendar]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

ArrowHead294 at 02:00, 16 November 2024

2024-11-16T02:00:26Z

← Older revision		Revision as of 02:00, 16 November 2024
Line 12:		Line 12:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3.5		\| 2.3.5
Line 35:		Line 27:
	\| 0.2500		\| 0.2500
	\| 7.33		\| 7.33
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
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	\|-		\|-
	\| 4		\| 4
	\| 93\352<br>(5\352)		\| 93\352<br />(5\352)
	\| 317.05<br>(17.05)		\| 317.05<br />(17.05)
	\| 6/5<br>(126/125)		\| 6/5<br />(126/125)
	\| [[Quadritikleismic]]		\| [[Quadritikleismic]]
	\|-		\|-
	\| 4		\| 4
	\| 117\352<br>(29\352)		\| 117\352<br />(29\352)
	\| 398.86<br>(98.86)		\| 398.86<br />(98.86)
	\| 34/27<br>(18/17)		\| 34/27<br />(18/17)
	\| [[World calendar]]		\| [[World calendar]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

FloraC: Review

2024-01-01T11:48:00Z

Review

← Older revision		Revision as of 11:48, 1 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~352et~~ is consistent to the [[7-odd-limit]]. Using the patent val, it tempers out ~~156250000/155649627, [[33554432/33480783~~]]~~, 359661568/358722675 and~~ [[2401/2400]] ~~in the 7-limit;~~ [[~~214990848~~/~~214358881~~]]~~, 78121827/77948684, 100663296/100656875, 10333575/10307264, 2097152/2096325, 1366875/1362944, 125000/124509~~, [[~~536870912~~/~~535869675~~]], ~~151263/151250, 104857600/104825259,~~ [[~~131072~~/~~130977~~]]~~, 1265625/1261568,~~ [[~~200704~~/~~200475~~]], ~~5788125~~/~~5767168~~, [[19712/19683~~]], 1479016/1476225, [[3025/3024~~]], [[41503/41472]], [[~~532400~~/~~531441~~]] ~~and 67110351/67108864~~ in the 11-limit. It [[support]]s [[world calendar]], [[septiruthenic]], [[enki]] and [[fortune]].		352edo is [[consistent]] to the [[7-odd-limit]]. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[2401/2400]], [[15625/15552]], [[390625/388962]], and [[33554432/33480783]] in the 7-limit; [[3025/3024]], 4375/4356, 14700/14641, [[19712/19683]], [[41503/41472]], and [[131072/130977]] in the 11-limit. It [[support]]s [[newt]], [[world calendar]], [[septiruthenic]], [[enki]] and [[fortune]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	352 factors into 2<sup>5</sup> × 11, with subset edos {{EDOs\|2, 4, 8, 11, 16, 22, 32, 44, 88, and 176}}~~. [[2112edo]], which sextuples it, gives a good correction to the harmonic 11~~.		352 factors into 2<sup>5</sup> × 11, with subset edos {{EDOs\| 2, 4, 8, 11, 16, 22, 32, 44, 88, and 176 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|[[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal<br>8ve Stretch (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	! colspan="2" \|Tuning Error		! colspan="2" \| Tuning Error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	~~\|2.3~~		\| 2.3.5
	~~\|{{monzo\|279 -176}}~~		\| 15625/15552, {{monzo\| 95 -57 -2 }}
	~~\|{{mapping\|352 558}}~~		\| {{mapping\| 352 558 817 }}
	~~\| -0.1002~~
	~~\| 0.1002~~
	~~\| 2.94~~
	\|-
	\|2.3.5
	\|15625/15552, {{monzo\|95 -57 -2}}
	\|{{mapping\|352 558 817}}
	\| +0.0891		\| +0.0891
	\| 0.2801		\| 0.2801
	\| 8.22		\| 8.22
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|2401/2400, 15625/15552, ~~359661568~~/~~358722675~~		\| 2401/2400, 15625/15552, 33554432/33480783
	\|{{mapping\|352 558 817 988}}		\| {{mapping\| 352 558 817 988 }}
	\| +0.1242		\| +0.1242
	\| 0.2500		\| 0.2500
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	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(reduced)~~*		! Generator*
	! Cents~~<br>(reduced)~~*		! Cents*
	! Associated<br>Ratio*		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|35\352		\| 35\352
	\|119.32		\| 119.32
	\|15/14		\| 15/14
	\|[[Septidiasemi]]		\| [[Septidiasemi]]
	\|-		\|-
	\|1		\| 1
	\|65\352		\| 65\352
	\|221.59		\| 221.59
	\|8388608/7381125		\| 8388608/7381125
	\|[[Fortune]]		\| [[Fortune]]
	\|-		\|-
	\|1		\| 1
	\|93\352		\| 93\352
	\|317.05		\| 317.05
	\|6/5		\| 6/5
	\|[[Hanson]]		\| [[Hanson]]
	\|-		\|-
	\|1		\| 1
	\|103\352		\| 103\352
	\|351.14		\| 351.14
	\|49/40		\| 49/40
	\|[[Newt]]		\| [[Newt]]
	\|-		\|-
	\|4		\| 4
	\|93\352<br>(5\352)		\| 93\352<br>(5\352)
	\|317.05<br>(17.05)		\| 317.05<br>(17.05)
	\|6/5<br>(126/125)		\| 6/5<br>(126/125)
	\|[[Quadritikleismic]]		\| [[Quadritikleismic]]
			\|-
			\| 4
			\| 117\352<br>(29\352)
			\| 398.86<br>(98.86)
			\| 34/27<br>(18/17)
			\| [[World calendar]]
	\|}		\|}

	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

Francium: Created page with "{{Infobox ET}} {{EDO intro|352}} == Theory == 352et is consistent to the 7-odd-limit. Using the patent val, it tempers out 156250000/155649627, 33554432/33480783, 359..."

2023-12-22T20:25:02Z

Created page with "{{Infobox ET}} {{EDO intro|352}} == Theory == 352et is consistent to the 7-odd-limit. Using the patent val, it tempers out 156250000/155649627, 33554432/33480783, 359..."

New page

{{Infobox ET}}
{{EDO intro|352}}

== Theory ==
352et is consistent to the [[7-odd-limit]]. Using the patent val, it tempers out 156250000/155649627, [[33554432/33480783]], 359661568/358722675 and [[2401/2400]] in the 7-limit; [[214990848/214358881]], 78121827/77948684, 100663296/100656875, 10333575/10307264, 2097152/2096325, 1366875/1362944, 125000/124509, [[536870912/535869675]], 151263/151250, 104857600/104825259, [[131072/130977]], 1265625/1261568, [[200704/200475]], 5788125/5767168, [[19712/19683]], 1479016/1476225, [[3025/3024]], [[41503/41472]], [[532400/531441]] and 67110351/67108864 in the 11-limit. It [[support]]s [[world calendar]], [[septiruthenic]], [[enki]] and [[fortune]].

=== Prime harmonics ===
{{Harmonics in equal|352}}

=== Subsets and supersets ===
352 factors into 25 × 11, with subset edos {{EDOs|2, 4, 8, 11, 16, 22, 32, 44, 88, and 176}}. [[2112edo]], which sextuples it, gives a good correction to the harmonic 11.

== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal 8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|279 -176}}
|{{mapping|352 558}}
| -0.1002
| 0.1002
| 2.94
|-
|2.3.5
|15625/15552, {{monzo|95 -57 -2}}
|{{mapping|352 558 817}}
| +0.0891
| 0.2801
| 8.22
|-
|2.3.5.7
|2401/2400, 15625/15552, 359661568/358722675
|{{mapping|352 558 817 988}}
| +0.1242
| 0.2500
| 7.33
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods per 8ve
! Generator (reduced)*
! Cents (reduced)*
! Associated Ratio*
! Temperaments
|-
|1
|35\352
|119.32
|15/14
|[[Septidiasemi]]
|-
|1
|65\352
|221.59
|8388608/7381125
|[[Fortune]]
|-
|1
|93\352
|317.05
|6/5
|[[Hanson]]
|-
|1
|103\352
|351.14
|49/40
|[[Newt]]
|-
|4
|93\352 (5\352)
|317.05 (17.05)
|6/5 (126/125)
|[[Quadritikleismic]]
|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct